Push a shopping cart, and it rolls forward. Stop pushing, and it eventually comes to rest. Kick a football, and it flies through the air. Jump off a diving board, and you fall into the pool. These everyday experiences all involve forces, and understanding forces is the key to understanding why motion happens the way it does.
Isaac Newton figured this out over 300 years ago, and his three laws of motion still explain everything from car crashes to rocket launches, from planetary orbits to the swing of a pendulum. Forces are what change motion, and momentum is what keeps motion going.
A force is a vector quantity that causes or tends to cause a change in the state of motion of an object, or causes deformation of the object. Force has both magnitude and direction.
The SI unit of force is the newton (N), defined as the force required to give a mass of one kilogram an acceleration of one meter per second squared: 1 N = 1 kg·m/s²
Forces can be contact forces (requiring physical contact between objects) or field forces (acting at a distance, like gravity or electromagnetic forces).
Statement: Every object continues in its state of rest or uniform motion in a straight line unless acted upon by a net external force.
This is also called the law of inertia.
If you slide a hockey puck across the ice, it eventually stops. So why does Newton say objects keep moving at constant velocity without a force?
The answer lies in friction. Friction is a force, and it's what slows the puck down. Without friction—on a perfectly smooth, frictionless surface—it really would keep moving forever at the same speed in the same direction.
Inertia is the tendency of a body to resist changes in its state of motion. The mass of an object is a quantitative measure of its inertia. A loaded truck has far more inertia than a bicycle.
Statement: The rate of change of momentum of a body is directly proportional to the net force applied to it and takes place in the direction of the net force.
F_net = dp/dt (general form)
F_net = ma (for constant mass)
This law reveals three fundamental relationships:
Example 1: A 1200 kg car accelerates from rest at 2.5 m/s². What net force acts on it?
F_net = ma = (1200)(2.5) = 3000 N
Example 2: You push a 50 kg box with 200 N horizontally, but kinetic friction opposes with 80 N. Find the acceleration.
F_net = 200 - 80 = 120 N
a = F_net/m = 120/50 = 2.4 m/s²
Statement: When object A exerts a force on object B, object B simultaneously exerts an equal and opposite force on object A.
F_AB = -F_BA
Key points about action-reaction pairs:
Examples:
A free body diagram (FBD) is a simplified representation showing all external forces acting on a single object, with the object represented as a point.
To construct a proper FBD:
ΣF = 0
ΣF_x = 0 ΣF_y = 0
An object in equilibrium is either:
p = mv
p = momentum (kg·m/s), m = mass (kg), v = velocity (m/s)
Momentum is a vector quantity with the same direction as velocity.
Alternative form of Newton's second law: F_net = dp/dt
This shows that net force equals the rate of change of momentum.
Example: A 2000 kg truck at 5 m/s has momentum 10,000 kg·m/s — the same as a 500 kg car at 20 m/s.
J = Δp = F_avg Δt
J = impulse (N·s or kg·m/s)
Impulse-Momentum Theorem: F_avg Δt = Δp = m(v - u)
This explains automotive safety features. Crumple zones and airbags increase Δt, which decreases F_avg, reducing forces on passengers.
Example: A 0.15 kg baseball at 40 m/s is struck by a bat and rebounds at 50 m/s in the opposite direction. Contact time is 0.002 s. Find average force.
Δp = m(v_f - v_i) = (0.15)(-50 - 40) = -13.5 kg·m/s
F_avg = Δp/Δt = -13.5/0.002 = -6750 N (magnitude 6750 N)
Σp_before = Σp_after
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
In a closed, isolated system (no external forces), total momentum before an interaction equals total momentum after.
This principle is valid regardless of the complexity of internal forces, making it extremely powerful for analyzing collisions and explosions.
Both momentum and kinetic energy are conserved.
Examples: Ideal gas molecules, billiard balls (nearly)
Momentum conserved, kinetic energy not conserved.
Some KE transforms to heat, sound, deformation.
Objects stick together after impact.
Maximum kinetic energy loss consistent with momentum conservation.
Energy loss in collisions: ΔKE = KE_initial - KE_final
This energy isn't destroyed but transforms into thermal energy, sound, and permanent deformation.
| Quantity | Symbol | Unit | Formula |
|---|---|---|---|
| Force | F | N | F = ma |
| Momentum | p | kg·m/s | p = mv |
| Impulse | J | N·s | J = F_avgΔt = Δp |
| Weight | W | N | W = mg |